Problem: What is $\vec a + \vec b$ ? $\begin{align*} \vec a &= 4 \hat\imath - 3 \hat\jmath \\ \vec b &= 1 \hat\imath + 7 \hat\jmath \end{align*}$ {1} {2} {3} {4} {5} {6} {7} {8} {9} {\llap{-}2} {\llap{-}3} {\llap{-}4} {\llap{-}5} {\llap{-}6} {\llap{-}7} {\llap{-}8} {\llap{-}9} {1} {2} {3} {4} {5} {6} {7} {8} {9} {\llap{-}2} {\llap{-}3} {\llap{-}4} {\llap{-}5} {\llap{-}6} {\llap{-}7} {\llap{-}8} {\llap{-}9} \vec a \vec b
Sum the $\hat\imath$ and $\hat\jmath$ components separately. $\vec a + \vec b = (4 + 1) \hat\imath + (-3 + 7) \hat\jmath$ $\hphantom{\vec a + \vec b} = 5\hat\imath + 4\hat\jmath$